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Universal outlier detection

机译：通用异常值检测

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摘要

The following outlier detection problem is studied in a universal setting. Vector observations are collected each with M coordinates. When the i-th coordinate is the outlier, the observations in that coordinate are assumed to be distributed according to the “outlier” distribution, distinct from the common “typical” distribution governing the observations in all the other coordinates. Nothing is known about the outlier and the typical distributions except that they are distinct and have full supports. The goal is to design a universal detector to best discern the outlier coordinate. A universal detector is proposed and is shown to be universally exponentially consistent, and a single-letter characterization of the exponent for a symmetric error criterion achievable by this detector is derived. An upper bound for the error exponent that applies to any universal detector is also derived. For the special case of M = 3, a tighter upper bound is derived that quantifies the loss in the exponent when the knowledge of the outlier and typical distributions is absent, from when they are known.
机译：在通用环境下研究以下异常值检测问题。收集的向量观测值各有M个坐标。当第i个坐标是异常值时，假定该坐标中的观测值是根据“异常值”分布来分配的，这不同于控制所有其他坐标中的观测值的常见“典型”分布。关于异常值和典型分布，除了它们是独特的并且有完整的支持以外，我们一无所知。目的是设计一种通用检测器，以最好地识别离群坐标。提出了一种通用检测器，该通用检测器显示为通用指数一致的，并且得出了该检测器可实现的对称误差准则的指数的单字母特征。还得出适用于任何通用检测器的误差指数的上限。对于M = 3的特殊情况，可以得出一个更严格的上限，从已知值开始，当不知道异常值和典型分布时，可以量化指数损失。

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